Energy and the Environment Physical Chemistry for Environmental Science Majors Leonard J. Soltzberg Simmons College, Boston, MA02115 Post-secondary programs dealing with the environment are proliferating in response to public concern about environmental issues and the consequent erowth of the environmental technology industry. ' h e 1934 Peterson's Guide to Four-Year Colleges lists 340 majors in environmental fields ( I ) . There are several categories of college-level environmcntnl programs, as dis&rd in thc nc&npanying paper hs Hortman and Soitzbrrc. wownms rolled .'en\+ - Thosr . ronmental science" usually are true science concentrations but are broader in disciplinary scope than a traditional chemistry major. Under the curriculum guidelines in place a t many institutions, it is impossible to require all the science courses that would be desirable in such a program. In the environmental science major a t our institution, two casualties of the imposed limit on courses in a major were physical chemistry and calculus. Our normal two-semester .ohvsical " chemistw" seauence . requires three semesters of calculus, and, because our environmental science major alreadv " reauires . the maximum allowed number of courses, it is impossible to inrludr ihrse impoltanr rourses. 'This o a w r drirrilwi our solution to this problem. Wr have created a single course that covers the major topics of applied thermodynamics and, through the use of computer modeling software, allows students to learn the concepts of differential and integral calculus without spending the time required to master the mechanics of differentiation and integration. Energy and the Environment Resigned to having only one semester to cover physical chemistry in the context of'environmental problems, we decided t h a t bulk-scale thermodynamics generally was more relevant than molecular quantum mechanics. Because many pressing environmental issues are directly or indirectly related to energy production and consumption (for example, acid rain, global warming, thermal pollution, nuclear waste, petroleum depletion), the topic of energy seemed like a n appropriate focus that could serve a s a platform for the discussion of the underlying science. Further, because environmental systems virtually always are dynamic, nonequilibrinm systems, we felt i t was important to include a treatment of the behavior of dynamic systems. Major Topics of the Course in Order of Presentation Basic Thermodynamics-energy, enthalpy, entropy, engines, Carnat cycle, efficiency, calorimetly,free energy, electroehemieal cells Dynamic System-quilibrium, steady states, stability, oscillation,chaos Energy Systems-(1) energy produdion: fossil fuels, nuclear energy, solar energy, (2) energy consumption: transportation, domestic, industrial Earth's Energy Balance-energy budget for Earth, anthropogenie influences, climate models.
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This topic list is a curious mix of the theoretical and the applied as well a s the classical and the contemporary. The
reader mav well wonder what book could be used for a course covkring such a n eclectic mix. The students purchased three items that formed the bulk of the readingmaterial, supplemented by articles of current interest that they and the professor supplied a s encountered. The Books Required
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Smith, Brian. Basic Chemical Thermodynamics,4th ed., Oxford University Press: New York, 1990.
Energy for Planet Earth the single topic issue of Scientific American 1990,263(31, 54. Acursory glance a t the Smith book shows the typical formulations of thermodynamics: work as defined by -PdV, the proof that entropy is a state function by taking the cyclic integral around a closed path, and so forth. The Harte book, while starting out with simple "back of the envelope" warm-UD exercises.. a a d u a t e s to svstems involvine coupled differential equations and eigenvalue problems. How can we hope to investigate this material oroductivelv with students who have notstudied calculus?'
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Calculus via Computer Modeling Our approach to the conundrum described in the previous o a r a a a ~ hwas to make extensive use of the computer kod&ng program, STELLA I1 (2).STELLAII is desiened to model dvnamic svstems. Because chanpe is the id&tifying feature of a dGamio system and anrntrinsic characteristic of environmental systems, we introduced the concepts of calculus i n the context of systems uudergoing change. While our students had not previously studied calculus, they were perfectly comfortable with the ideas of rate of change (such a s a rate of population growth or rate of flow) and of cumulative change (such a s the accumulation of a pollutant i n a body of water). STELLA I1 makes such concepts graphically clear, and attaching the standard calculus notation of differentials and integrals posed no dificultv. What was left out, of course, was the mechanics of taking derivatives or inteaals. We certainlv do not sueeest that i t would not be preFerable for our students to Tiam these methods. But. under the time constraints imposed bv the structure of the major, using the computer to ko the actual labor allowed u s to explore systems and ideas that would otherwise have been completely inaccessible. We were able to discuss eauilibrium. steadv states, stability. .. and even chaos in dynamic systenm As an example of the power of this approach, we have included a student's STELLAII solution to one of the hour exam problems-to plot the Lorenz attractor, the solution to a set of coupled differential equations (Figs. 1and 2 ) . This model was produced by a student after the seventh week of the course. Volume 72 Number 11 November 1995
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Figure 1. STELLA II model for the Lorenz equations, a set of three coupled differential equations that can display chaotic behavior (3.
Figure 2. Output of the STELLA 11 model in Figure 1, showing the resulting chaotic anractor projected along two different axes
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Journal of Chemical Education
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Amlications t o Environmental Problems During the course of the semester, we created STELLA I1 models for many of the systems described in the Harte book. The useofthese rompuwr mudclsallowed the students to get :i hands-on ferling tiw the dynamir rhararrer o f e n r r ~ y flows, responses of complex systems to perturbations, as well as the dangers of modeling. We emphasized the lurking possibility of computational errors and artifacts, and by the end of the term, the students were exercising critical judgement in their construction of new models. Laboratory The laboratory component of this course focused on quantitative measurements relating to energy systems. Experiments included calorimetric measurement of the heat content of coal and fuel oil; measurement of the energy content of various dry cells by discharging through a known resistor and monitoring the voltage with a computer data acquisition system; construction of a lead-acid rechargeable battery and performance measurements on
the battery; and monitoring of solar flux using a calibrated silicon photocell and a stripchart recorder. Some laboratory periods were devoted to field trips to a commercial wind plant, a cogeneration plant, and and an energy-efflcient public building. Summarv The compromises inherent in a n interdepartmental Environmental Science major have led us to develop a novel one-semesterjunior-level course covering thermodynamics and the fundamental concepts of calculus. Extensive use of computer-based modeling is key to the success of this approach. Special laboratory experiments complement the course material Literature Cited 1. Pelarsonb FovrYeor Colieg~8.24thed.: P6nceton:Petenon's Guides, 1993. 2, STELLAII, High Performance Systems, h e . , 45 Lyme Road, Suite 300. Hanouer. NH 03755. 3. See, for example, Tagg. S. L.: LeMaster, C. L.: LeMaster, C. B.: MeQuarrie, D. A. J. Chem. Educ. 1994. 71.363-374 end references therein.
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